Ergodic Theory and Dynamical Systems

Research Article

Automorphisms of the Bernoulli endomorphism and a class of skew-products

William Parrya1

a1 Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK


We consider a class of skew-products with base the one-sided two-shift equipped with the (½, ½)Bernoulli measure and fibre either or the circle. We give conditions for the first kind to be isomorphic to the base itself and use this result to establish an isomorphism with the base for the second kind when a certain irrationalis very well approximated by rationals. A consequence is that there is a circle action of automorphisms commuting with theone-sided two-shift.

(Received June 29 1995)